The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order frequencies are necessary to model the gravitational-wave signal observed by a distant observer in binary black hole merger simulations. In this talk, I will show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of non-linear modes.